相关论文: Generalized probabilities taking values in non-Arc…
The quantum gravity has great difficulties with application of the probability notion. In given article this problem is analyzed according to algorithmic viewpoint. According to A.N. Kolmogorov, the probability notion can be connected with…
As a fundamental structure in real-world networks, in addition to graph topology, communities can also be reflected by abundant node attributes. In attributed community detection, probabilistic generative models (PGMs) have become the…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As a by-product, we provide a version for lower probabilities of the Strong Law of Large Numbers.
We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of…
We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…
After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on…
The purpose of this article is to define and study new invariants of topological spaces: the $p$-adic Betti numbers and the $p$-adic torsion. These invariants take values in the $p$-adic numbers and are constructed from a virtual pro-$p$…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
We review several known categorification procedures, and introduce a functorial categorification of group extensions with applications to non-abelian group cohomology. Categorification of acyclic models and of topological spaces are briefly…
We estimate several probability distributions arising from the study of random, monic polynomials of degree $n$ with coefficients in the integers of a general $p$-adic field $K_{\mathfrak{p}}$ having residue field with $q= p^f$ elements. We…
In this paper, we will incorporation the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bososnic and fermionic theories with Lifshitz scaling based on generalized uncertainty…
The fiducial coincides with the posterior in a group model equipped with the right Haar prior. This result is here generalized. For this the underlying probability space of Kolmogorov is replaced by a $\sigma$-finite measure space and…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
In this work, we will introduce the notion of generalized topological groups using generalized topological structure and generalized continuity defined by ?A. Cs?asz?ar [2]. We will discuss some basic properties of this kind of structures…
For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…